Question

If the equation of the parabola is $x^2=-8y$, then

• A. focus is $(0,-2)$
• B. directrix is $y=2$
• C. length of latusrectum is 8
• D. All of the above

Answer 1

Answer: (D)

The given equation is of the form $x^2=-4ay$, where $a$ is positive.
Therefore, the focus is on $Y$-axis in the negative direction arid parabula uperis downiwards.
Comparing the given equation with standard form, we get $a=2$.
Therefore, the coordinates of the focus are $(0,-2)$ and the the equation of directrix is $y=2$ and the length of the latusrectum is $4a$, i.e., 8 .